Schmidt's conjecture on normality for commuting matrices.
Semigroup-valued multiplicative functions
Sequences and dynamical systems associated with canonical approximation by rationals
Sequences with small discrepancy relative to n events
Sets of block structure and discrepancy estimates
S-expansions in dimension two
The technique of singularization was developped by C. Kraaikamp during the nineties, in connection with his work on dynamical systems related to continued fraction algorithms and their diophantine approximation properties. We generalize this technique from one into two dimensions. We apply the method to the the two dimensional Brun’s algorithm. We discuss, how this technique, and related ones, can be used to transfer certain metrical and diophantine properties from one algorithm to the others. In...
Shifted values of the largest prime factor function and its average value in short intervals
We obtain estimates for the average value of the largest prime factor P(n) in short intervals [x,x+y] and of h(P(n)+1), where h is a complex-valued additive function or multiplicative function satisfying certain conditions. Letting stand for the sum of the digits of n in base q ≥ 2, we show that if α is an irrational number, then the sequence is uniformly distributed modulo 1.
Sidon basis in polynomial rings over finite fields
Let denote the polynomial ring over , the finite field of elements. Suppose the characteristic of is not or . We prove that there exist infinitely many such that the set contains a Sidon set which is an additive basis of order .
Simultane diophantische Approximationen abhängiger Größen in mehreren Metriken
Simultaneous Diophantine approximation and asymptotic formulae on manifolds
Simultaneous inhomogeneous Diophantine approximation of the values of integral polynomials with respect to Archimedean and non-Archimedean valuations
We prove an analogue of the convergence part of Khintchine’s theorem for the simultaneous inhomogeneous Diophantine approximation on the Veronese curve with respect to the different valuations. It is an extension of the author’s earlier results.
Singularité des produits de Anzai associés aux fonctions caractéristiques d'un intervalle
Small digitwise perturbations of a number make it normal to unrelated bases.
Soma Estimates of the H...-Uniform Distribution.
Some applications of Elliot's mean-value theorem.
Some asymptotic results associated with a generalized Gauss-Kuzmin-type operator.
Some asymptotic results on extended sequences connected with the regular continued fraction.
Some Distribution Properties of 0,1-Sequences.
Some doubly exponential sums over ℤₘ
Some explicit constructions of sets with more sums than differences